Author: VoijaRisa

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Data: Stellar Quadrant Observations – 9/18/2020

Last time I went out observing, I met a Will Day, an photographer with quite a bit of experience in astrophotography. He asked if he could photograph Yseult and I as we worked and it ended up with one of the coolest images to come out of this project. But as cool as it was, it didn’t feel quite right since we were using the red headlamps and wearing mundane clothes with the period instrument.

Fortunately, Will was game to try something more planned to really capture the period feel. So Yesult and I went out last month, putting on our best late period garb. The results were beyond what I expected.

If you’ve ever wondered what it feels like to do this observing, this is it.  Continue reading “Data: Stellar Quadrant Observations – 9/18/2020”

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Almagest Book V: Model for the Second Anomaly

In the last chapter, we introduced an instrument capable of determining the ecliptic latitude and longitude of an object so long as the position of the true sun or fixed star is known. Using this on the moon, Ptolemy found

that the distance of the moon from the sun was sometimes in agreement with that calculated from the above [Book IV] hypothesis, and sometimes in disagreement, the discrepancy being at some times small and at other times great.

How so? Ptolemy provides details. Continue reading “Almagest Book V: Model for the Second Anomaly”

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Almagest Book V: On the Use of an Astrolabe

Now that Ptolemy has described how to construct an astrolabe, he covers its usage. Specifically, Ptolemy begins when

both sun and moon could be observed above the earth at the same time.

As a brief reminder, what Ptolemy is really discussing here is what was necessary for him to make the observations that revealed the moon’s second anomaly. So what is given here is really in that context. As such, neither the sun nor moon is actually required for use of this instrument. In this case, Ptolemy is using the sun to align the instrument for use, and considering the moon to be the target, hence why the sun and moon are required. But, as we’ll see, a star can be used for alignment and there’s no reason one couldn’t be used as a target either.

Continue reading “Almagest Book V: On the Use of an Astrolabe”

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Almagest Book V: On the Construction of an Astrolabe

Book IV was all about setting up a preliminary lunar model with a single anomaly which Ptolemy modeled using the epicyclic model. But throughout, Ptolemy kept referencing a second anomaly he discovered, without ever saying how. In his introduction to Book V, Ptolemy finally gives the answer:

We were led to awareness of and belief in this [second anomaly] by the observations of lunar positions recorded by Hipparchus, and also by our own observations, which were made by means of an instrument which we constructed for this purpose.

That instrument was, at the time, called an “astrolabe” which simply means “for taking the [position of] stars,”1 but today we would call it an armillary sphere. Ptolemy describes how one should be constructed which is what we’ll be exploring in this post. To help us, here’s the image of one labeled from Toomer’s translation2.

Continue reading “Almagest Book V: On the Construction of an Astrolabe”

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Almagest Book IV: Hipparchus’ Two Values of Lunar Anomaly Second Triad

In the last post, we followed Ptolemy as he reviewed three eclipses Hipparchus used to determine the parameters for his model showing they were different from Ptolemy’s. In this post, we’ll repeat the procedure for the second set of three eclipses, again showing that Hipparchus’ calculations did not match those of Ptolemy.

Continue reading “Almagest Book IV: Hipparchus’ Two Values of Lunar Anomaly Second Triad”

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Almagest Book IV: Table of Lunar Equation of Anomaly (First Anomaly)

Although I don’t see any particular reason we couldn’t have done this several chapters earlier, Ptolemy has elected to hold off producing his table of Lunar Anomaly until almost the very end of Book IV3.

At the end of the previous chapter, he did toss in a few expository notes on this table noting that this will be useful in the future for “calculations concerning conjunctions and oppositions”4. To do so, Ptolemy doesn’t show his math, but notes that it was done “geometrically, in the same way as we already did for the sun.”

However, to use that method requires knowing the ratio of the radius of the deferent to that of the epicycle. Ptolemy states he takes a ratio of $60:5 \frac{1}{4}$. Using that, he calculates his table in the same manner as he did for the sun, which is in $6º$ intervals near apogee and $3º$ intervals near perigee. However, because this epicycle rotates opposite the direction of the deferent, we should subtract if the angle is in the first column, and add if it is in the second5

That being laid out, the table is below: Continue reading “Almagest Book IV: Table of Lunar Equation of Anomaly (First Anomaly)”

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Almagest Book IV: Determining the Lunar Epoch for Latitude

Now that we’ve squared away the most accurate motion in latitude Ptolemy can muster, it’s time to use it to reverse calculate the lunar latitude at the beginning of the epoch, but to do so, we’ll need to calculate the precise position in latitude at some point in time. To do so, Ptolemy again turns to eclipses, with all the same considerations as the last post, except we want ones at opposite nodes instead of near the same one. Continue reading “Almagest Book IV: Determining the Lunar Epoch for Latitude”

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Data: Stellar Quadrant Observations – 8/21/2020

This week a thin crescent moon set early along with clear skies and pleasant evening temperatures set up another another promising night of observing. I was joined again by Their Excellency Yseult and we headed back out to the Danville Conservation Area. While a bit more of a drive, the impressively dark skies are certainly worth it as it opens up opportunities to add stars that we couldn’t see elsewhere to the catalog. Surprisingly, the nice night didn’t attract many other observers, but an astrophotographer named Will Day stopped by with his wife and child who had never been to the site before. He asked if we minded being included in pictures and we happily agreed. I think the results turned out well.

Overall, we took observations on 36 stars and the three visible planets that night, most of which we took turns observing as we could then use each of our results as a quick reality check against one another and hopefully produce better results. Continue reading “Data: Stellar Quadrant Observations – 8/21/2020”

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Almagest Book IV: Correcting the Lunar Mean Motion in Latitude

Previously, we looked at how Ptolemy made corrections to the anomalistic motion for his lunar model. In this post, we’ll be doing something similar for the mean motion of lunar latitude.

Ptolemy explained that the value we originally noted was in error,

because we too adopted Hipparchus’ assumptions that [the diameter of] the moon goes approximately 650 times into its own orbit, and $2 \frac{1}{2}$ times into [the diameter of] the Earth’s shadow, when it is at mean distance in the syzygies.

In short, Hipparchus’ figures were a good starting point but now we can do better by

using more elegant methods which do not require any of the previous assumptions for the solution of the problem.

Continue reading “Almagest Book IV: Correcting the Lunar Mean Motion in Latitude”